Just started the game, maybe I can help out. Explorer of an Old World you can get when you just rescued Delvin and Salvador. You are in the ruins of an old house, sleeping bags on the right bottom of the screen. You need to search the container behind it, or look at it or something.

Insignificant Details I got when making a mistake. When you need to get Dr. Braun to your friend Salvador you feed him spiced food, and poison him with orange juice and wine cooler. If you forgot to switch the signs at the restroom and the storage room, you'll get the achievement.

No Shame was a really easy one as well. Where you have to disarm the bomb, use the skip button instead of solving it =]

Farewell... If you have found dead Lissa, just use the "look at" action on her body and the achievement will unlock.

When you arrive in the ruins with Delvin and Salvador (after you rescued them), there's a desk on the left of your screen, there's a digital diary on it. And instead of reading it, you need to wipe it clean, without reading it.